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Please give me the link to some paper, website or book that you know about which discusses in detail some experiments which quantitatively verify Maxwell's 4th equation, which is $$\quad \nabla\times{\bf B} = \frac{1}{ c^2}\frac{\partial{\bf E}}{\partial t} + \mu_0{\bf J}$$

I am specially interested in the case where the electric field is constant and where Maxwell's equation becomes

$$\quad \nabla\times{\bf B} = \mu_0{\bf J}.$$

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    $\begingroup$ Raja, please check how the curvature of the wire and by this the acceleration of the charges induces the magnetic field. $\endgroup$
    – HolgerFiedler
    Commented Dec 3, 2015 at 17:09

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A permanent current flowing through an electrical coil produces a magnetic field inside the coil : this is a direct consequence of Maxwell's fourth equation.

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    $\begingroup$ Yes. Thanks. But i am asking about the detailed analysis. I accept that current causes magnetism, and the magnetic fields curls around the wire, as seen in pictures where magnetic fillings form pattern around current carrying wires. But i don't find intuitive is the fact that the summation of magnetic field around a closed loop must always equal a given function of current., as stated by maxwell $\endgroup$
    – Prem
    Commented Dec 3, 2015 at 14:38
  • $\begingroup$ All of us who routinely use electromagnets are scratching our heads - the resulting magnetic field clearly is (within hysteresis) a given function of current. What motivates this doubt? $\endgroup$
    – Jon Custer
    Commented Dec 3, 2015 at 15:02
  • $\begingroup$ Yes, from general experience we know that magnetic field is 'proportional' to the current. But it is not clear to me why for a current wire the line integral of magnetic field around every current element should be the same irrespective of how we twist the wire. For example the law holds even if i twist the wires however i desire. This is why i was asking for conforming experiments. It is interesting that biot savart's experiments conform Ampere's law for steady current. I am trying to understand why that is so right now. $\endgroup$
    – Prem
    Commented Dec 5, 2015 at 14:33

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